Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales

被引：1

作者：

Agarwal, Ravi P. ^{[1
]}

Darwish, Mohamed Abdalla ^{[2
]}

Elshamy, Hamdi Ali ^{[2
]}

Saker, Samir H. ^{[3
,4
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] Damanhour Univ, Fac Sci, Dept Math, Damanhour 22514, Egypt

[3] Mansoura Univ, Dept Math, Mansoura 35516, Egypt

[4] New Mansoura Univ, Fac Sci, Dept Math, New Mansoura City 7723730, Egypt

来源：

AXIOMS | 2024年 / 13卷 / 02期

关键词：

Muckenhoupt classes; Gehring classes; time scales; Holder's inequality; Jensen's inequality; chain rule; NORM INEQUALITIES; MAXIMAL FUNCTIONS; HARDY; INTEGRABILITY; FACTORIZATION;

D O I：

10.3390/axioms13020098

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new.

引用

页数：25

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